For which value of $k$, lines $x+2y=9$ and $kx+4y=-5$ are parallel?

Two lines are parallel when the coefficients of $x$ and $y$ are in the same ratio. For $x+2y=9$ and $kx+4y=-5$, $\dfrac{1}{k}=\dfrac{2}{4}$ $\Rightarrow 4=2k$ $\Rightarrow k=2$ The same thing using slopes: the first line has slope $-\dfrac{1}{2}$ and the second has slope $-\dfrac{k}{4}$. $-\dfrac{k}{4}=-\dfrac{1}{2}$ $\Rightarrow k=2$